A diplomatic push to end Israel's nearly weeklong offensive in the Gaza Strip gained momentum Tuesday, with Egypt's president predicting that airstrikes would end within hours and Israel's prime minister saying his country would be a "willing partner" to a cease-fire with the Islamic militant group Hamas.

As international diplomats raced across the region to cement a deal, a senior Hamas official said an agreement was close even as relentless airstrikes and rocket attacks between the two sides continued. The Israeli death toll rose to five with the deaths Tuesday of an Israeli soldier and a civilian contractor. More than 130 Palestinians have been killed.

"We haven't struck the deal yet, but we are progressing and it will most likely be tonight," Moussa Abu Marzouk said Tuesday from Cairo, where cease-fire talks were being held.

Israeli officials were more circumspect, saying only that "intensive efforts" were under way to end the fighting. Israeli media quoted Defence Minister Ehud Barak as telling a closed meeting that Israel wanted a 24-hour test period of no rocket fire to see if Hamas could enforce a truce.

In what appeared to be a last-minute burst of heavy fire, Israeli tanks and gunboats shelled targets late Tuesday, and an airstrike killed two brothers riding on a motorcycle. The men weren't identified.

The fighting came shortly before U.S. Secretary of State Hillary Rodham Clinton was set to arrive. President Barack Obama dispatched her to the Mideast from Cambodia, where she had accompanied him on a visit.

Egyptian President Mohammed Morsi, perhaps the most important interlocutor between Hamas, which rules the Palestinian territory, and the Israelis, said the negotiations between the two sides would yield "positive results" during the coming hours.

Israel demands an end to rocket fire from Gaza and a halt to weapons smuggling into Gaza through tunnels under the border with Egypt. It also wants international guarantees that Hamas will not rearm or use Egypt's Sinai region, which abuts both Gaza and southern Israel, to attack Israelis.

Hamas wants Israel to halt all attacks on Gaza and lift tight restrictions on trade and movement in and out of the territory that have been in place since Hamas seized Gaza by force in 2007. Israel has rejected such demands in the past.

In Brussels, a senior official of the European Union's foreign service said a cease-fire would include an end of Israeli airstrikes and targeted killings in Gaza, the opening of Gaza crossing points and an end to rocket attacks on Israel. The official spoke on condition of anonymity because he was not authorized to speak to the media.